Centre Number Candidate Number General Certificate of Secondary Education January 2015 Mathematics Unit T2 (With calculator) Foundation Tier [GMT21] FRIDAY 9 JANUARY, 9.15 am 10.45 am *GMT21* *GMT21* TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. You must answer the questions in the spaces provided. Do not write outside the box, around each page, on blank pages or tracing paper. Complete in blue or black ink only. Do not write with a gel pen. Answer all twenty-eight questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You may use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 100. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Functional Elements will be assessed in this paper. Quality of written communication will be assessed in Questions 7 and 16. You should have a calculator, ruler, compasses and a protractor. The Formula Sheet is on page 2. *28GMT2101* *28GMT2101*
Formula Sheet Area of trapezium = 1 2 (a + b)h a h b Volume of prism = area of cross section length cross section length *28GMT2102* *28GMT2102*
BLANK PAGE (Questions start overleaf) [Turn over *28GMT2103* *28GMT2103*
1 (a) Write down the next two prime numbers after 53 (b) Find the cube root of 27 Answer, [2] Answer [1] *28GMT2104* *28GMT2104*
2 The table below gives information on the sports played by boys after school. Sport Football Rugby Hockey Tennis Number of boys 26 8 12 14 Angle Draw a clearly labelled pie chart for this information. [4] [Turn over *28GMT2105* *28GMT2105*
3 27 girls did a test. The stem and leaf diagram shows their marks. 0 1 3 4 1 4 4 5 6 2 0 1 3 5 7 7 3 2 4 4 6 6 6 4 4 5 8 9 5 0 0 3 5 key 1 4 means 14 marks (a) Find (i) the mode of the marks, Answer [1] (ii) the median of the marks, Answer [1] (iii) the range of the marks. Answer [1] *28GMT2106* *28GMT2106*
The marks for 27 boys in the same test are shown. 12 12 24 26 26 26 27 30 35 36 36 38 39 39 40 42 43 44 47 52 54 56 56 58 58 59 59 (b) Complete a back to back stem and leaf diagram below for the boys. The first two rows of the marks have already been entered. Boys Girls 0 1 3 4 2 2 1 4 4 5 6 7 6 6 6 4 2 0 1 3 5 7 7 9 9 8 6 6 5 0 3 2 4 4 6 6 6 4 4 5 8 9 5 0 0 3 5 key 2 1 means 12 marks key 1 4 means 14 marks [2] (c) By using the stem and leaf diagram decide whether the boys or girls did better in the test. Give a reason for your answer. The did better in the test because [2] [Turn over *28GMT2107* *28GMT2107*
4 A fish tank is a cuboid. The tank has a length of 9 metres, a width of 4 metres and a height of 3 metres. The fish tank is filled with 99m 3 of water. What is the depth of water in the tank? Answer metres [2] 5 The Eurostar train leaves London at 11 24 (London time) and arrives in Paris at 14 47 (Paris time). The time in Paris is 1 hour ahead of the time in London. How long does the journey take? Answer [3] *28GMT2108* *28GMT2108*
6 Work out the size of the angle w. 98 diagram not drawn accurately 143 66 w Answer w = [3] [Turn over *28GMT2109* *28GMT2109*
Quality of written communication will be assessed in this question. 7 A smartphone costs 375 Jill pays a deposit of 95 for this smartphone. She then pays 35 each month. How many months will it take before she has paid for the smartphone? Show your working clearly. Answer months [3] *28GMT2110* *28GMT2110*
8 (a) Explain the meaning of 3 4 Answer [1] (b) Calculate 3 4 5 3 Answer [1] (c) Calculate 4.2 2 + 361. Answer [2] 9 (a) Find the value of 5x + 6y when x = 9 and y = 2 Answer [2] (b) Solve 7x 9 = 47 Answer x = [2] (c) In the spaces provided, write down the next two numbers in the sequence 23, 21, 17, 11,, [2] [Turn over *28GMT2111* *28GMT2111*
10 The triangle shown is isosceles. ABC is a straight line. 64 diagram not drawn accurately A B s C Work out the size of the angle s. Answer s = [3] *28GMT2112* *28GMT2112*
11 (a) Complete the table for y = 5 3x x 1 0 1 2 3 y = 5 3x 8 2 4 [2] (b) Using values from the table, draw the graph of y = 5 3x y 8 6 4 2 3 2 1 0 1 2 3 x 2 4 6 [1] [Turn over *28GMT2113* *28GMT2113*
12 The table shows the engine size (litres) of different cars and the distance (km) that the cars can travel on one litre of petrol. Engine size 1.0 1.8 2.4 1.2 2.1 1.5 2.7 Distance 12 8.6 5 9.4 5.9 10.2 3.8 (a) Draw a scatter graph. [2] 12 10 8 Distance (km) 6 4 2 0 0 1 2 3 Engine size (litres) (b) Draw a line of best fit. [1] *28GMT2114* *28GMT2114*
(c) Another car travels 7 km on one litre of petrol. Use your line of best fit to estimate the engine size of this car. Answer litres [1] (d) Describe the correlation in this scatter graph. Answer [1] 13 The diagram shows a regular pentagon placed on top of a regular hexagon. diagram not drawn accurately e Calculate the size of the angle marked e. Show all your working. Answer e = [4] [Turn over *28GMT2115* *28GMT2115*
14 ABCD is a parallelogram. Angle DAB = 125 Angle ADB = 37 Angle CEB = 51 D 37 x C diagram not drawn accurately E 51 A 125 B Calculate the size of the angle x. Answer x = [4] 15 Factorise (a) 8x + 12 Answer [1] (b) x 2 + 7x Answer [1] *28GMT2116* *28GMT2116*
Quality of written communication will be assessed in this question. 16 Joanne is having a party. She needs forty packets of crisps. A single packet of crisps costs 30 pence in each of two local stores. Each store has a special offer on packets of crisps. Bargain Store 20% off every ten packets Discount Store buy 3 and get one more free Which is better value? Show your working clearly. Answer [4] [Turn over *28GMT2117* *28GMT2117*
17 Complete the spaces (a), (b), (c) and (d) on the electricity bill. Meter Reading Northern Electricity Date Current units Previous units Units used Price per unit Total ( ) 30 June 43458 42763 (a) 15 pence (b) VAT @ 5% (c) Total Charge (d) [5] 18 (a) Write the recurring decimal 0.375375375... using dot notation. Answer [1] (b) Write 0.28 correct to 4 decimal places. Answer [1] *28GMT2118* *28GMT2118*
19 (a) A toy lorry has 6 wheels and a toy car has 4 wheels. Write down an expression for the total number of wheels on x lorries and y cars. Answer [2] (b) Write down the first 3 terms of the sequence whose n th term is n 2 + 3 Answer,, [2] 20 P is the point (2, 3) and Q is the point ( 4, 1). Work out the coordinates of the midpoint of the line PQ. Answer (, ) [2] [Turn over *28GMT2119* *28GMT2119*
21 The masses of some stones found on a beach are shown in the table. Mass (g) Number of stones 10 < m < 20 33 20 < m < 30 88 30 < m < 40 57 40 < m < 50 52 50 < m < 60 43 60 < m < 70 17 70 < m < 80 10 (a) Which interval contains the median mass? Answer [1] (b) Draw a frequency polygon to represent the data. [4] *28GMT2120* *28GMT2120*
22 (a) Simplify 2 22 8, leaving your answer in index form. Answer [1] (b) Expand and simplify 4(x 2) + 3(2x + 3) Answer [2] [Turn over *28GMT2121* *28GMT2121*
23 In a group of golfers there are 37 males and 23 females. 19 of the males are wearing glasses and 14 of the females are wearing glasses. What percentage of the group are wearing glasses? Answer % [3] 24 Write 600 as a product of prime factors. Express your answer in index notation. Answer [3] *28GMT2122* *28GMT2122*
25 The diagram shows a semicircle inside a rectangle. 5.5 cm 11 cm Work out the area of the shaded region. Answer cm 2 [3] [Turn over *28GMT2123* *28GMT2123*
26 A sheet of paper measures 297mm by 210mm. Work out the length between diagonally opposite corners. Answer mm [3] *28GMT2124* *28GMT2124*
27 (a) Write an expression, in terms of x, for the perimeter of the trapezium shown. Give your answer in its simplest form. x + 6 x x 2x + 3 Answer [2] (b) The perimeter of this trapezium is 34cm. (i) Using the perimeter, write down an equation in terms of x. Equation [1] (ii) Solve the equation to find x. Answer x = [1] [Turn over *28GMT2125* *28GMT2125*
28 A solution to the equation x 3 4x = 26 lies between 3 and 4 Use trial and improvement to solve this equation. Give your answer correct to 1 decimal place. Show each stage of your working. x x 3 4x Answer x = [3] *28GMT2126* *28GMT2126*
THIS IS THE END OF THE QUESTION PAPER *28GMT2127* *28GMT2127*
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